ODE
\[ y'(x)^3=a+b x \] ODE Classification
[_quadrature]
Book solution method
Missing Variables ODE, Dependent variable missing, Solve for \(y'\)
Mathematica ✓
cpu = 0.0452425 (sec), leaf count = 80
\[\left \{\left \{y(x)\to \frac {3 (a+b x)^{4/3}}{4 b}+c_1\right \},\left \{y(x)\to c_1-\frac {3 \sqrt [3]{-1} (a+b x)^{4/3}}{4 b}\right \},\left \{y(x)\to \frac {3 (-1)^{2/3} (a+b x)^{4/3}}{4 b}+c_1\right \}\right \}\]
Maple ✓
cpu = 0.063 (sec), leaf count = 68
\[ \left \{ y \left ( x \right ) ={\frac {3}{4\,b} \left ( bx+a \right ) ^{{\frac {4}{3}}}}+{\it \_C1},y \left ( x \right ) ={\frac {{\frac {3\,i}{8}} \left ( -\sqrt {3}+i \right ) }{b} \left ( bx+a \right ) ^{{\frac {4}{3}}}}+{\it \_C1},y \left ( x \right ) ={\frac {{\frac {3\,i}{8}} \left ( \sqrt {3}+i \right ) }{b} \left ( bx+a \right ) ^{{\frac {4}{3}}}}+{\it \_C1} \right \} \] Mathematica raw input
DSolve[y'[x]^3 == a + b*x,y[x],x]
Mathematica raw output
{{y[x] -> (3*(a + b*x)^(4/3))/(4*b) + C[1]}, {y[x] -> (-3*(-1)^(1/3)*(a + b*x)^(4/3))/(4*b) + C[1]}, {y[x] -> (3*(-1)^(2/3)*(a + b*x)^(4/3))/(4*b) + C[1]}}
Maple raw input
dsolve(diff(y(x),x)^3 = b*x+a, y(x),'implicit')
Maple raw output
y(x) = 3/4*(b*x+a)^(4/3)/b+_C1, y(x) = 3/8*I*(b*x+a)^(4/3)*(-3^(1/2)+I)/b+_C1, y(x) = 3/8*I*(b*x+a)^(4/3)*(3^(1/2)+I)/b+_C1